Q: A submarine is submerged at a depth of 30 m in seawater (density $$\rho = 1025\ \text{kg/m}^3). $$What is the total pressure experienced by the submarine, assuming standard atmospheric pressure at sea level ($$P_{atm} = 101.3\ \text{kPa}$$)? Use $$g = 9.8\ \text{m/s}^2.$$

$$P = P_{atm} + \rho g d = 101.3\ \text{kPa} + (1025\ \text{kg/m}^3)(9.8\ \text{m/s}^2)(30\ \text{m}) = 402.05\ \text{kPa}$$

Q: A sealed tank contains oil ($$\rho = 900\ \text{kg/m}^3) to a $$depth of 5 m. The air above the oil has been completely removed. What is the pressure at the bottom of the tank?

$$P = \rho g d = (900\ \text{kg/m}^3)(9.8\ \text{m/s}^2)(5\ \text{m}) = 44,100\ \text{Pa}$$

Q: A diver descends to a depth of 20 m in freshwater ($$\rho = 1000\ \text{kg/m}^3). $$What is the increase in pressure due to the water alone?

$$\Delta P = \rho g d = (1000\ \text{kg/m}^3)(9.8\ \text{m/s}^2)(20\ \text{m}) = 196,000\ \text{Pa}$$

Q: A tank is filled with mercury ($$\rho = 13,600\ \text{kg/m}^3) to a $$depth of 2 m. What is the gauge pressure at the bottom of the tank?

$$P = \rho g d = (13,600\ \text{kg/m}^3)(9.8\ \text{m/s}^2)(2\ \text{m}) = 266,560\ \text{Pa}$$

Q: A water tower is open to the atmosphere and supplies water to a town. If the water level in the tower is 15 m above ground, what is the pressure at the base of the tower due to the water alone? ($$\rho = 1000\ \text{kg/m}^3$$, $$g = 9.8\ \text{m/s}^2)$$

$$P = \rho g d = (1000\ \text{kg/m}^3)(9.8\ \text{m/s}^2)(15\ \text{m}) = 147,000\ \text{Pa}$$

Q: A diver at 10 m depth in seawater ($$\rho = 1025\ \text{kg/m}^3) $$experiences a total pressure of approximately double the atmospheric pressure. Which calculation supports this statement?

$$P = P_{atm} + \rho g d = 101,300\ \text{Pa} + (1025\ \text{kg/m}^3)(9.8\ \text{m/s}^2)(10\ \text{m}) = 201,750\ \text{Pa}$$

Q: If the atmospheric pressure is $$101,300\ \text{Pa}$$ and the pressure at a certain depth in a fluid is $$250,000\ \text{Pa}$$, what is the gauge pressure at that depth?

$$P_{gauge} = P_{total} - P_{atm} = 250,000\ \text{Pa} - 101,300\ \text{Pa} = 148,700\ \text{Pa}$$

Question 1

A submarine is submerged at a depth of 30 m in seawater (density $$ho = 1025\ 	ext{kg/m}^3). $$What is the total pressure experienced by the submarine, assuming standard atmospheric pressure at sea level ($$P_{atm} = 101.3\ 	ext{kPa}$$)? Use $$g = 9.8\ 	ext{m/s}^2.$$

Accepted Answer

$$P = P_{atm} + ho g d = 101.3\ 	ext{kPa} + (1025\ 	ext{kg/m}^3)(9.8\ 	ext{m/s}^2)(30\ 	ext{m}) = 402.05\ 	ext{kPa}$$

Question 2

Which of the following best explains why fluid pressure increases with depth?

Accepted Answer

The weight of the fluid above exerts a force due to gravity, increasing pressure with depth.

Question 3

A sealed tank contains oil ($$ho = 900\ 	ext{kg/m}^3) to a $$depth of 5 m. The air above the oil has been completely removed. What is the pressure at the bottom of the tank?

Accepted Answer

$$P = ho g d = (900\ 	ext{kg/m}^3)(9.8\ 	ext{m/s}^2)(5\ 	ext{m}) = 44,100\ 	ext{Pa}$$

Question 4

Three containers of different shapes but equal base area are filled with water to the same depth. The air above the water is removed, so surface pressure is zero. Which statement is correct about the pressure at the bottom of each container?

Accepted Answer

The pressure at the bottom is the same for all containers because pressure depends only on depth, not shape.

Question 5

A diver descends to a depth of 20 m in freshwater ($$ho = 1000\ 	ext{kg/m}^3). $$What is the increase in pressure due to the water alone?

Accepted Answer

$$\Delta P = ho g d = (1000\ 	ext{kg/m}^3)(9.8\ 	ext{m/s}^2)(20\ 	ext{m}) = 196,000\ 	ext{Pa}$$

Question 6

If a glass beaker contains a liquid with density $$\rho$$, and you imagine a cylinder of liquid inside with cross-sectional area $$A$$ and height $$d$$, what is the mass of this cylinder?

Accepted Answer

$$m = \rho A d$$

Question 7

A tank is filled with mercury ($$ho = 13,600\ 	ext{kg/m}^3) to a $$depth of 2 m. What is the gauge pressure at the bottom of the tank?

Accepted Answer

$$P = ho g d = (13,600\ 	ext{kg/m}^3)(9.8\ 	ext{m/s}^2)(2\ 	ext{m}) = 266,560\ 	ext{Pa}$$

Question 8

In hydrostatic equilibrium, which statement is true about the pressure at points of equal depth in a connected fluid?

Accepted Answer

The pressure is the same at all points of equal depth in a connected fluid.

Question 9

A water tower is open to the atmosphere and supplies water to a town. If the water level in the tower is 15 m above ground, what is the pressure at the base of the tower due to the water alone? ($$ho = 1000\ 	ext{kg/m}^3$$, $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$P = ho g d = (1000\ 	ext{kg/m}^3)(9.8\ 	ext{m/s}^2)(15\ 	ext{m}) = 147,000\ 	ext{Pa}$$

Question 10

A container is filled with a fluid of density $$\rho to a $$depth $$d. If $$atmospheric pressure is $$P_{atm}$$, what is the total pressure at the bottom of the container?

Accepted Answer

$$P = P_{atm} + \rho g d$$

Question 11

A diver at 10 m depth in seawater ($$ho = 1025\ 	ext{kg/m}^3) $$experiences a total pressure of approximately double the atmospheric pressure. Which calculation supports this statement?

Accepted Answer

$$P = P_{atm} + ho g d = 101,300\ 	ext{Pa} + (1025\ 	ext{kg/m}^3)(9.8\ 	ext{m/s}^2)(10\ 	ext{m}) = 201,750\ 	ext{Pa}$$

Question 12

If the atmospheric pressure is $$101,300\ 	ext{Pa}$$ and the pressure at a certain depth in a fluid is $$250,000\ 	ext{Pa}$$, what is the gauge pressure at that depth?

Accepted Answer

$$P_{gauge} = P_{total} - P_{atm} = 250,000\ 	ext{Pa} - 101,300\ 	ext{Pa} = 148,700\ 	ext{Pa}$$

Question 13

A fluid is at rest in a container. Which of the following is NOT a factor affecting the pressure at a given depth?

Accepted Answer

The shape of the container

Question 14

A tank contains two layers: oil ($$ho = 900\ 	ext{kg/m}^3$$, depth = 2 m) on top of water ($$ho = 1000\ 	ext{kg/m}^3$$, depth = 3 m). What is the total pressure at the bottom, ignoring atmospheric pressure?

Accepted Answer

$$P = ho_{oil} g d_{oil} + ho_{water} g d_{water} = (900\ 	ext{kg/m}^3)(9.8\ 	ext{m/s}^2)(2\ 	ext{m}) + (1000\ 	ext{kg/m}^3)(9.8\ 	ext{m/s}^2)(3\ 	ext{m}) = 17,640\ 	ext{Pa} + 29,400\ 	ext{Pa} = 47,040\ 	ext{Pa}$$

Question 15

A glass beaker contains water ($$ho = 1000\ 	ext{kg/m}^3) to a $$depth of 8 m. What is the total pressure at the bottom if the beaker is open to the atmosphere ($$P_{atm} = 101,300\ 	ext{Pa}$$)?

Accepted Answer

$$P = P_{atm} + ho g d = 101,300\ 	ext{Pa} + (1000\ 	ext{kg/m}^3)(9.8\ 	ext{m/s}^2)(8\ 	ext{m}) = 179,900\ 	ext{Pa}$$

Question 16

If the density of a fluid is doubled, what happens to the pressure at a given depth (assuming atmospheric pressure is unchanged)?

Accepted Answer

The pressure due to the fluid at that depth doubles.

Question 17

A diver is at a depth $$d in a $$fluid of density $$\rho. $$Which equation gives the pressure due to the fluid at that depth?

Accepted Answer

$$P = \rho g d$$

Question 18

A tank is filled with water ($$ho = 1000\ 	ext{kg/m}^3) to a $$depth of 12 m. If the tank is sealed and the air above the water is evacuated, what is the pressure at the bottom?

Accepted Answer

$$P = ho g d = (1000\ 	ext{kg/m}^3)(9.8\ 	ext{m/s}^2)(12\ 	ext{m}) = 117,600\ 	ext{Pa}$$

Fluid Pressure and Depth: Physics with Calculus Study Notes

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